The explosion went off at about 10.30 pm at a market outside the Marco Polo hotel, a place Duterte visits often and used for meetings during a campaign for a May election that he won by a huge margin. He typically spends his weekends in Davao.
Police said 67 people were wounded in addition to the 14 dead.
Duterte, the mayor of Davao City for more than two decades, said the blast late on Friday outside a high-end hotel intensified what was an "extraordinary time" in the Philippines, and security forces would redouble efforts to tackle crime, drugs and insurgency.
There was no claim of responsibility.
Duterte canceled a trip to Brunei on Saturday in what would have been his first overseas visit as president.